Pythagorean Theorem Calculator

What is the Pythagorean theorem?

The Pythagorean theorem describes the sides of a right-angled triangle. It states that the square of the hypotenuse — the longest side, opposite the right angle — equals the sum of the squares of the other two sides, the legs: a² + b² = c². It only applies to right triangles.

How to use it

To find the hypotenuse from the two legs, square each leg, add them, and take the square root: c = √(a² + b²). To find a missing leg when you know the hypotenuse and one leg, subtract instead: b = √(c² − a²). The hypotenuse is always the longest side, so a leg must be shorter than it.

Example

A right triangle with legs of 3 and 4 has a hypotenuse of √(3² + 4²) = √25 = 5 — the well-known 3-4-5 triangle. Going the other way, if the hypotenuse is 13 and one leg is 5, the other leg is √(13² − 5²) = √144 = 12.